PolygonsSet

PolygonsSet

The leaf nodes of the BSP tree must have a
Boolean attribute representing the inside status of
the corresponding cell (true for inside cells, false for outside
cells). In order to avoid building too many small objects, it is
recommended to use the predefined constants
Boolean.TRUE and Boolean.FALSE

PolygonsSet

The boundary is provided as a collection of sub-hyperplanes. Each sub-hyperplane has the
interior part of the region on its minus side and the exterior on
its plus side.

The boundary elements can be in any order, and can form
several non-connected sets (like for example polygons with holes
or a set of disjoint polyhedrons considered as a whole). In
fact, the elements do not even need to be connected together
(their topological connections are not used here). However, if the
boundary does not really separate an inside open from an outside
open (open having here its topological meaning), then subsequent
calls to the checkPoint method will not be meaningful anymore.

If the boundary is empty, the region will represent the whole
space.

Parameters:

boundary - collection of boundary elements, as a
collection of SubHyperplane objects

PolygonsSet

The boundary is provided as a list of points considering to
represent the vertices of a simple loop. The interior part of the
region is on the left side of this path and the exterior is on its
right side.

This constructor does not handle polygons with a boundary
forming several disconnected paths (such as polygons with holes).

Polygons with thin pikes or dents are inherently difficult to handle because
they involve lines with almost opposite directions at some vertices. Polygons
whose vertices come from some physical measurement with noise are also
difficult because an edge that should be straight may be broken in lots of
different pieces with almost equal directions. In both cases, computing the
lines intersections is not numerically robust due to the almost 0 or almost
π angle. Such cases need to carefully adjust the hyperplaneThickness
parameter. A too small value would often lead to completely wrong polygons
with large area wrongly identified as inside or outside. Large values are
often much safer. As a rule of thumb, a value slightly below the size of the
most accurate detail needed is a good value for the hyperplaneThickness
parameter.

Parameters:

hyperplaneThickness - tolerance below which points are considered to
belong to the hyperplane (which is therefore more a slab)

buildNew

This method allow to create new instances without knowing
exactly the type of the region. It is an application of the
prototype design pattern.

The leaf nodes of the BSP tree must have a
Boolean attribute representing the inside status of
the corresponding cell (true for inside cells, false for outside
cells). In order to avoid building too many small objects, it is
recommended to use the predefined constants
Boolean.TRUE and Boolean.FALSE. The
tree also must have either null internal nodes or
internal nodes representing the boundary as specified in the
getTree method).

getVertices

The polygon boundary can be represented as an array of loops,
each loop being itself an array of vertices.

In order to identify open loops which start and end by
infinite edges, the open loops arrays start with a null point. In
this case, the first non null point and the last point of the
array do not represent real vertices, they are dummy points
intended only to get the direction of the first and last edge. An
open loop consisting of a single infinite line will therefore be
represented by a three elements array with one null point
followed by two dummy points. The open loops are always the first
ones in the loops array.

If the polygon has no boundary at all, a zero length loop
array will be returned.

All line segments in the various loops have the inside of the
region on their left side and the outside on their right side
when moving in the underlying line direction. This means that
closed loops surrounding finite areas obey the direct
trigonometric orientation.

Returns:

vertices of the polygon, organized as oriented boundary
loops with the open loops first (the returned value is guaranteed
to be non-null)